In order to enhance the efficiency, increase the power density and minimize the relative size of a rotating electric machine (such as an electric motor and a power generator), a permanent magnet is used as a constant magnetic source. With the development in processing and materials, the permanent magnet with high magnetic energy product is widely used in rotating electric machines.
When a permanent magnet is used as a constant magnetic source rotating without a load, the characteristics in the magnetic flux path of the rotating electric machine are controlled by the constant magnetic field. During rotation, the equivalent magnetic reluctance in the magnetic flux path changes periodically based on the rotating angle. A magnetic reluctance torque, also referred to as stop torque, is caused due to the rate of change of the magnetic reluctance in response to the rotating angle and is proportional to the square of the equivalent magnetic flux in the air gap. The torque generated by the constant magnetic field from the permanent magnet in order to match the minimum equivalent magnetic reluctance in the magnetic flux path of the core is referred to as a cogging torque.
When the driving torque is not much larger than the cogging torque, an undesired output torque ripple is generated to cause vibration and noise and further affect the control precision, especially when rotating at a very low rate. The cogging torque in a rotating electric machine is expressed as:
      T    cog    =            -              1        2              ⁢          ϕ      2        ⁢                  ⅆ                  R          mag                            ⅆ        θ            wherein Tcog is the cogging torque; φ is the equivalent magnetic flux in the air gap; Rmag is the equivalent magnetic reluctance in the magnetic flux path; and θ is the rotating angle.
The change of equivalent magnetic reluctance in the magnetic flux path can be expressed as a periodical function of the rotating angle. Accordingly, the cogging torque is the equivalent magnetic reluctance in the magnetic flux path differentiated by the rotating angle. Alternatively, the cogging torque can also be expressed as a symmetric period function of the rotating angle, which can be expressed in Fourier series.
To minimize the effect of the cogging torque on the rotating electric machine, two methods can be used. The first method is to reduce the equivalent magnetic flux in the air gap. The output cogging torque is proportional to the square of the equivalent magnetic flux in the air gap and the equivalent magnetic flux in the air gap is proportional to the effective output magnetic torque. Reducing the equivalent magnetic flux in the air gap does not only minimize the cogging torque but also reduce the effective output magnetic torque. Therefore, such a method is seldom used to minimize the cogging torque.
The second method is to reduce the rate of change of the equivalent magnetic reluctance in the magnetic flux path in response to the rotating angle. Ideally, as long as the equivalent magnetic reluctance in the magnetic flux path is kept constant during rotation (that is to say, the rate of change is zero), no cogging torque will be generated. Related designs concerning the reduction of the rate of change of the equivalent magnetic reluctance in the magnetic flux path in response to the rotating angle are capable of preventing negative influences on the effective output magnetic torque and other characteristics of the rotating electric machine. Therefore, such a method is often used to minimize the cogging torque.
There are many factors that cause the equivalent magnetic reluctance in the magnetic flux path to change. Mainly, the change of the magnetic flux path due to the relative rotating movement between the tooth slot structure of the armature core disposed for accommodating the winding and the magnetic pole core causes the change of the equivalent magnetic reluctance in the magnetic flux path. For example, the transition of the magnetic pole corresponding to the tooth, the magnetic reluctance in the air gap due to the slot opening, the change of the magnetic flux intensity and magnetic saturation directly or indirectly cause the change of the equivalent magnetic reluctance in the magnetic flux path, leading to the cogging torque.
To eliminate the change of the equivalent magnetic reluctance in the magnetic flux path, a skew tooth slot or a skew magnetic pole can be used to select one from the tooth slot of the armature and the magnetic pole of the permanent magnet to generate a phase shift due to the change of the axial magnetic reluctance by continuously or piecewise rotating a specific angle so that the total change of the magnetic reluctance is reduced, leading to a reduced total cogging torque. However, such a method using skew rotation results in increased cost and time in manufacturing, assembly and inspection.
Alternatively, the cogging torque can be reduced by using a specific ratio of the amount of slots to the amount of magnetic poles. Generally, the larger the lowest common multiple of the amount of slots and the amount of magnetic poles, the smaller the cogging torque. Using such a specific ratio, restricted windings are required and, sometimes, undesired radial forces occur. For example, for a rotating electric machine comprising 9 slots and 8 magnetic poles, a radial force occurs for such a slot-to-pole ratio, which causes radial loading on the bearing and leads to vibration and noise. Therefore, such a method is not suitable for low-vibration and low-noise applications.
Alternatively, a rotating electric machine can comprise multiple magnetic pole cores or multiple armature cores to reduce the cogging torque. The multiple magnetic pole cores or multiple armature cores are used to cause two cogging torques with the same intensity and an electrical angle different of 180 degrees so as to balance off the cogging torque during rotation. However, such a design is only useful for a rotating electric machine really requiring multiple magnetic pole cores or multiple armature cores. Moreover, such a design results in increased cost and time in manufacturing, assembly and inspection.
Alternatively, another method is to reduce the change of the total equivalent magnetic reluctance by changing the surface or internal structure of the tooth shoe of the armature core for adjacent air gaps or changing the surface or internal structure of the magnetic pole for adjacent air gaps. For example, the number of the slots on the tooth shoe surface can be increased to enlarge the surface arc. Alternatively, the tooth shoe can comprise materials with different permeability. Alternatively, the arc of the surface-mounted magnet can be changed. Alternatively, the magnetic pole can comprise materials with different permeability. All these approaches can suppress the change of the total equivalent magnetic reluctance.
Therefore, it is crucial to minimize the cogging torque for a rotating electric machine with ordinary manufacturing processing without additional manufacturing cost and time.